This invention relates to embedding electronic structure in controllable quantum systems.
Adiabatic quantum computing (AQC) works by changing the Hamiltonian of a controllable quantum system from an initial Hamiltonian whose ground state is easy to prepare into a Hamiltonian whose ground state encodes the solution of a computationally interesting problem. The speed of this algorithm is determined by the adiabatic theorem of quantum mechanics which states that an eigenstate remains at the same position in the eigenspectrum if a perturbation acts on the system sufficiently slowly. Simply embedding a computational problem in a Hamiltonian suitable for AQC does not ensure an efficient solution. The required runtime for the adiabatic evolution depends on the energy gap between the ground state and first excited state at the smallest avoided crossing.
AQC has been applied to classical optimization problems such as search engine ranking, protein folding, and machine learning. There is an equivalence between a large set of such computational problems (problems in the complexity class NP) and a set of models in classical physics (e.g., classical Ising models with random coupling strengths). For some AQC-based quantum computers, solutions of these computational problems are based on the NP-Completeness of determining the ground state energy of classical Ising spin glasses. In general, quantum computing, including AQC, does not necessarily provide efficient solutions to NP-Complete problems in the worst case. However, there may exist sets of instances of some NP-Complete problems for which AQC can find the ground state efficiently, but which defy efficient classical solution by any means.
Some quantum computers implemented as a controllable quantum systems that use some principles of AQC, but deviate from the requirement of being strictly confined to the ground state at zero temperature and may have considerable thermal mixing of higher lying states. Such quantum computers are sometimes referred to as quantum annealing computers. Medium scale (e.g., 500 qubit) quantum annealing computers have been investigated for many problems to determine if and by how much quantum annealing on the classical Ising model outperforms approaches using optimized codes on classical hardware for computing the same ground state solution.
Another form of quantum computing is the gate model (also known as the circuit model) of quantum computing. The gate model is based on a generalization of the classical gate model where a classical bit (i.e., a Boolean value of 0 or 1) is manipulated using logic gates. In the quantum gate model, a quantum bit or “qubit” (i.e., a quantum superposition of quantum basis states, such as a state representing a “0” and a state representing a “1”) is manipulated using quantum gates. While there is a form of computational equivalence for certain computations between the gate model and the AQC model, such that the computations can be performed in comparable amount of time using either model, different problems can be mapped more easily into a computation more suitable for one than the other. Also, the quantum systems that realize the gate model or the AQC model (including quantum annealing computers) may be very different. The molecular electronic structure problem (also known as “quantum chemistry”) is an example of a problem that has been mapped to the gate model, but not to the AQC model.